Wildcards in bash are referred to as pathname expansion. Pathname expansion is also sometimes referred to as globbing. Pathname expansion "expands" the "*", "?", and "[...]" syntaxes when you type them as part of a command, for example:

  $ ls *.jpg         # List all JPEG files
  $ ls ?.jpg         # List JPEG files with 1 char names (eg a.jpg, 1.jpg)
  $ rm [A-Z]*.jpg    # Remove JPEG files that start with a capital letter

A subtle point about pathname expansion that is not often understood is that it is done by bash and not by the operating system or by the program that is being run. The program never sees the wildcards, bash substitutes the expansion into the command line before running the program. This is rarely important except when you're writing code and calling exec() and friends: if you don't execute the program via bash any wildcards in the command line that you pass to exec() won't get expanded.

But these are not the only forms of wildcards supported by bash. The other forms are referred to as extended globbing and you must enable them before you can use them:

  $ shopt -s extglob

Extended globbing as described by the bash man page:

  ?(pattern-list)   Matches zero or one occurrence of the given patterns
  *(pattern-list)   Matches zero or more occurrences of the given patterns
  +(pattern-list)   Matches one or more occurrences of the given patterns
  @(pattern-list)   Matches one of the given patterns
  !(pattern-list)   Matches anything except one of the given patterns

Here a pattern-list is a list of items separated by a vertical bar "|" (aka the pipe symbol). If you look at these you can see why the leading character was chosen as it matches what is used in regular expression syntax:

  Bash              Regular Expression
  ?(pattern-list)   (...|...)?
  *(pattern-list)   (...|...)*
  +(pattern-list)   (...|...)+
  @(pattern-list)   (...|...)    [@ not a RE syntax]
  !(pattern-list)   "!" used as for negative assertions in RE syntax

Well, except for the "@" character you can see why...

For example, to list all the JPEG and GIF files that start with either "ab" or "def" you could do:

  $ ls +(ab|def)*+(.jpg|.gif)

Of course you could also do this without extended globbing:

  # ls ab*.jpg ab*.gif def*.jpg def*.gif

To list all the files that match the regular expression "ab(2|3)+.jpg" you could do:

  $ ls ab+(2|3).jpg

Now that's something you can't do with regular globbing. Note: this matches files like ab2.jpg, ab3.jpg, ab2222.jpg, ab333.jpg, etc.

However, probably the most interesting extended globbing syntax is the "!(...)" syntax for matching everything except (ie not matching). But, be careful, this doesn't always do what you might expect. For example, let's list all the files that aren't JPEGs or GIFs. One's first thought might be something like this:

  $ ls *!(.jpg|.gif)         # wrong, Wrong, WRONG

But that doesn't work because the ".jpg" and the ".gif" of any file's name end up getting matched by the "*" and the null string at the end of the file name is the part that ends up not matching the "!(...)" pattern. The correct syntax is:

  $ ls !(*.jpg|*.gif)

For a more complex negation example, let's go back to the first example and list all the files that aren't JPEG or GIF files and start with either "ab" or "def". This is actually quite simple, we just take the first example and nest it inside of "!(...)":

  $ ls !(+(ab|def)*+(.jpg|.gif))

Of course, like complex regular expressions, this will be completely incomprehensible 10 minutes after you write it.